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2010 | 20 | 4 | 763-771
Tytuł artykułu

Markov chain model of phytoplankton dynamics

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A discrete-time stochastic spatial model of plankton dynamics is given. We focus on aggregative behaviour of plankton cells. Our aim is to show the convergence of a microscopic, stochastic model to a macroscopic one, given by an evolution equation. Some numerical simulations are also presented.
Rocznik
Tom
20
Numer
4
Strony
763-771
Opis fizyczny
Daty
wydano
2010
otrzymano
2010-02-02
poprawiono
2010-06-01
Twórcy
  • Department of Biomathematics, Institute of Mathematics, Polish Academy of Sciences ul. Bankowa 14, 40-007 Katowice, Poland
Bibliografia
  • Adler, R. (1997). Superprocesses and plankton dynamics, Monte Carlo Simulation in Oceanography: Proceedings of the 'Aha Huliko'a Hawaiian Winter Workshop, Manoa, HI, pp. 121-128.
  • Aldous, D. (1999). Deterministic and stochastic models for coalescence (aggregation and coagulation): A review of the mean-field theory for probabilists, Bernoulli 5(1): 3-48.
  • Arino, O. and Rudnicki, R. (2004). Phytoplankton dynamics, Comptes Rendus Biologies 327(11): 961-969.
  • Clark, P. and Evans, F. (1954). Distance to nearest neighbor as a measure of spatial relationships in populations, Ecology 35(4): 445-453.
  • El Saadi, N. and Bah, A. (2007). An individual-based model for studying the aggregation behavior in phytoplankton, Ecological Modelling 204(1-2): 193-212.
  • Ethier, S.N. and Kurtz, T.G. (1986). Markov Processes: Characterization and Convergence, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, NY.
  • Franks, P.J.S. (2002). NPZ models of plankton dynamics: Their construction, coupling to physics, and application, Journal of Oceanography 58(2): 379-387.
  • Henderson, P.A. (2003). Practical Methods in Ecology, WileyBlackwell, Malden, MA.
  • Illian, J., Penttinen, A., Stoyan, H. and Stoyan, D. (2008). Statistical Analysis and Modelling of Spatial Point Patterns, John Wiley & Sons Ltd, Chichester.
  • Jackson, G. (1990). A model of the formation of marine algal flocs by physical coagulation processes, Deep-Sea Research 37(8): 1197-1211.
  • Laurençot, P. and Mischler, S. (2002). The continuous coagulation-fragmentation equations with diffusion, Archive for Rational Mechanics and Analysis 162(1): 45-99.
  • Levin, S.A. and Segel, L.A. (1976). Hypothesis for origin of planktonic patchiness, Nature 259.
  • Passow, U. and Alldredge, A. (1995). Aggregation of a diatom bloom in a mesocosm: The role of transparent exopolymer particles (TEP), Deep-Sea Research II 42(1): 99-109.
  • Rudnicki, R. and Wieczorek, R. (2006a). Fragmentationcoagulation models of phytoplankton, Bulletin of the Polish Academy of Sciences: Mathematics 54(2): 175-191.
  • Rudnicki, R. and Wieczorek, R. (2006b). Phytoplankton dynamics: from the behaviour of cells to a transport equation, Mathematical Modelling of Natural Phenomena 1(1): 83-100.
  • Rudnicki, R. and Wieczorek, R. (2008). Mathematical models of phytoplankton dynamics, Dynamic Biochemistry, Process Biotechnology and Molecular Biology 2 (1): 55-63.
  • Wieczorek, R. (2007). Fragmentation, coagulation and diffusion processes as limits of individual-based aggregation models, Ph.D. thesis, Institute of Mathematics, Polish Academy of Sciences, Warsaw, (in Polish).
  • Young, W., Roberts, A. and Stuhne, G. (2001). Reproductive pair correlations and the clustering of organisms, Nature 412(6844): 328-331.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv20i4p763bwm
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